Problem: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}6x-y &= -3 \\ -6x-y &= -9\end{align*}$
Solution: Begin by moving the $y$ -term in the second equation to the right side of the equation. $-6x = y-9$ Divide both sides by $-6$ to isolate $x$ $x = {-\dfrac{1}{6}y + \dfrac{3}{2}}$ Substitute this expression for $x$ in the first equation. $6({-\dfrac{1}{6}y + \dfrac{3}{2}}) - y = -3$ $-y + 9 - y = -3$ Simplify by combining terms, then solve for $y$ $-2y + 9 = -3$ $-2y = -12$ $y = 6$ Substitute $6$ for $y$ in the top equation. $6x- 6 = -3$ $6x-6 = -3$ $6x = 3$ $x = \dfrac{1}{2}$ The solution is $\enspace x = \dfrac{1}{2}, \enspace y = 6$.